% Same as smle_pairwise but with four drugs


clear
clc
% person, period, drugid, choice, copay, prev


% ignore serial correlations
% focus on class 2

% sketch
% fminsearch @ (t) SMLE(t, data, random_draws)
% SMLE function: simulate using random draws scaled by parameters
% compute a total likelihood of seeing data as a function of parameters
% Compute a Hessian of the function at optimal parameters



% personid quarter drugid chosen cost_sharing incumbent control_extra treat_extra
% starts in June 1996 (1)
% can go to May 2006 (40)
A = importdata('general_entry_choice_data_modified.txt');

data = A(:,1:6);
id = A(:,1);
quarter = A(:,2);
drugid = A(:,3);
chosen = A(:,4);
cost_sharing = A(:,5);
incumbent_id = A(:,6);

% % filtering
filter = (1-isnan(cost_sharing)); % CHANGED
id(filter == 0, :) = [];
quarter(filter == 0, :) = [];
drugid(filter == 0, :) = [];
chosen(filter == 0, :) = [];
cost_sharing(filter == 0, :) = [];
incumbent_id(filter == 0, :) = [];
data(filter == 0, :) = [];


% extra parameters: number of periods, etc.
num_drugs = max(drugid);
num_periods = max(quarter);
num_people = max(id);

% setup work common to each loop
[~,~,id] = unique([id quarter], 'rows'); % unique person/quarter combos => creates choice id
outside = 1 - accumarray(id, chosen); % chose the outside option


rho_grid = [-0.5 0.5];



for k=1:length(rho_grid)

    % Test some code in terms of simulated MLE
    % person, period, drugid, choice, copay, prev

    rho = rho_grid(k);
    rho


    % draw some normal random numbers
    rng(17)
    S = 100;
    
    % NEW
    %random_draws = normrnd(0,1,num_people*num_drugs, S);
    random_draws = zeros(num_people*num_drugs, S);
    
    mu = zeros(4,1);
    Sigma = [1 rho rho 0; rho 1 rho 0; rho rho 1 0; 0 0 0 1];
    
    for jj=1:S

        R = mvnrnd(mu,Sigma,num_people);
        R_reshaped = reshape(R',[num_people*num_drugs 1]); % reshape reads by column, so transpose it first
        random_draws(:,jj) = R_reshaped;
    end
    
    % from smle_pariwise_generic_correlated (assign generic Zocor the brand
    % Zocor value
    for i=1:num_people
       random_draws(num_drugs*(i-1)+4,:) = random_draws(num_drugs*(i-1)+1,:); 
    end
    

    % parameters delta for each drug x period, alpha, gamma, sigma2 (of idiosyncratic)
    % start with values that roughly reflect previous estimates
    %delta_init = [-1;-0.5;-2];
    delta_init = [-1.0970;-0.0839;-1.7948;-1.0970];
    %params_init = [delta_init; 0.04; 5; 1];
    gamma_init = [6.29 0 0 6.29; 0 5.56 0 0; 0 0 7.22 0; 0 0 0 3];
    params_init = [delta_init; 0.0284; gamma_init(:,1);gamma_init(:,2);gamma_init(:,3);gamma_init(:,4);-1.391];
    params = params_init;

    myopts = optimset('TolFun', 1e-10, 'MaxFunEvals', 12000, 'MaxIter',10000, 'display','iter'); % off, iter, final, notify
    % previously 10^-8

    % test
    SMLE_v2(params_init,data,random_draws,num_drugs,num_periods,id,outside,S);

    [params_opt, mle] = fminsearch (@(t)...
        -SMLE_v2(t,data,random_draws,num_drugs,num_periods,id,outside,S), params_init, myopts);


    delta = params_opt(1:4);

    alpha = params_opt(5);
    gamma = [params_opt(6:9) params_opt(10:13) params_opt(14:17) params_opt(18:21)];
    sigma = params_opt(22);

    alpha
    gamma
    sigma



    %% Compute standard errors
    fun = @(t) -SMLE_v2(t,data,random_draws, num_drugs, num_periods, id, outside, S);


    % hessian of a function at the final point
    %[H_small, H, H_big, G] = own_hessian_v2(fun, params_opt);
    [H_small, H, H_big, G] = own_hessian_v3(fun, params_opt);

    n=length(params_opt);
    for i=1:n
        for j=i+1:n
            H(i,j) = H(j,i);
            H_small(i,j) = H_small(j,i);
            H_big(i,j) = H_big(j,i);
        end
    end

    %variance_mat = inv(H_big);
    variance_mat = inv(H_small);
    standard_errors = diag(variance_mat.^(.5));



    se_gamma = [standard_errors(6:9) standard_errors(10:13) standard_errors(14:17) standard_errors(18:21)];

    gamma
    se_gamma
    mle

    save(['smle_generic_correlated_' num2str(k) '.mat']);

end
